# The Elliptic Curve secp256k1

Learn about the special elliptic curve secp256k1 and how it meets security requirements in this lesson.

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## Overview

A curve of special interest is the Koblitz curve **secp256k1** that is used in the Bitcoin ECDSA signature scheme. secp256k1 is a Certicom curve that‘s recommended by the

$p=2^{256}-2^{32}-2^{9}-2^{8}-2^{7}-2^{6}-2^{4}-1$

is a generalized Mersenne prime number. The curve equation is given in the short Weierstrass form $y^{2}=x^{3}+A x+B$, where $A=0$ and $B=7$; therefore, the curve has $j$-invariant $j=0$ by this corollary

$\# E\left(\mathbb{F}_{p}\right)=2^{256}-2^{129}-1$

thus, $E\left(\mathbb{F}_{p}\right)$ is cyclic by this corollary

$\begin{aligned} P=& 0279 B E 667 E F 9 D C B B A C 55 A 06295 C E 870 B 07 \\ & 029 B F C D B 2 D C E 28 D 959 F 2815 B 16 F 81798 \end{aligned}$

in the compressed form, having cofactor $h=01$. According to

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